What is the Relationship Between Velocity and Distance for a Sprinter?

[mbkau00]

y axis: velocity m/s
x axis: distance m

Graph models a sprinter over 100m

velocity is increasing in a straight line up to 25m from 0m/s to 12m/s, then is consistently between 12m/s and 11.8m/s for the remaining 75m.

I can calculate variables (time taken, average acceleration etc) for the remaining 75m or 50m as velocity isn't changing much.

I'm struggling to calculate the average acceleration over the first 15m and the approximate distance traveled during the first 5 seconds.

Thanks in advance for any help.

 

[Delphi51]

Welcome to PF!
It is highly unusual to graph velocity vs distance; we nearly always graph velocity vs time.
Are you sure it is velocity vs distance?
If it is, you will need calculus to work it out as the acceleration will not be constant over the first 12 seconds.
The straight line on v vs x means v = kx or dx/dt = kx.
Change it to dx/x = k*dt
Integrate both sides to get a relation between x and t.
Then you can find velocity dx/dt and acceleration dv/dt.

 

[mbkau00]

hi thanks for the welcome, and thanks for the reply!

Yes it is definitely a velocity vs distance.

Thanks again for your reply.